(i) 2/3 and 4/5

Let us make the denominators same, say 60

i.e., 2/3 and 4/5 can be written as:

2/3 = (2 × 20)/(3 × 20) = 40/60

4/5 = (4 × 12)/(5 × 12) = 48/60

Five rational numbers between 2/3 and 4/5 = five rational numbers between 40/60 and 48/60

Therefore, Five rational numbers between 40/60 and 48/60

= 41/60, 42/60, 43/60, 44/60, 45/60

(ii) -3/2 and 5/3

Let us make the denominators same, say 6

i.e., -3/2 and 5/3 can be written as:

-3/2 = (-3 × 3)/(2× 3) = -9/6

5/3 = (5 × 2)/(3 × 2) = 10/6

Five rational numbers between -3/2 and 5/3

= five rational numbers between -9/6 and 10/6

Therefore, Five rational numbers between -9/6 and 10/6

= -1/6, 2/6, 3/6, 4/6, 5/6

(iii) 1/4 and 1/2

Let us make the denominators same, say 24.

i.e., 1/4 and 1/2 can be written as:

1/4 = (1 × 6)/(4 × 6) = 6/24

1/2 = (1 × 12)/(2 × 12) = 12/24

Five rational numbers between 1/4 and 1/2

= five rational numbers between 6/24 and 12/24

Therefore, Five rational numbers between 6/24 and 12/24

= 7/24, 8/24, 9/24, 10/24, 11/24